Daily Archives: August 12, 2007

1-parameter subgroups of Lie groups

My first cut at this post was a fairly traditional introduction to one parameter subgroups of Lie groups. Along the way, I made this illustration showing the complicated global versus simple local behavior of one parameter subgroups:
One parameter subgroup illustration
But then, in writing down examples, I realized that the readers are likely to be intimately familiar with the multiplication of complex numbers, and so I decided to concentrate on the multiplication of nonzero complex numbers. These form a nice (real) 2-dimensional Lie group with very clear one-parameter subgroups.

So I decided to rewrite the post using simple examples only. You can get the abstract Lie theory from wikipedia, but I had to include the above illustration cause it’s too pretty to put in the bit bucket.

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